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Integrating Boolean and Mathematical Solving: Foundations, Basic Algorithms, and Requirements [chapter]

Gilles Audemard, Piergiorgio Bertoli, Alessandro Cimatti, Artur Korniłowicz, Roberto Sebastiani
2002 Lecture Notes in Computer Science  
doi:10.1007/3-540-45470-5_22 fatcat:zy5iy4ee2rfzzgml3frxgdngzq

Solving Immunology?

Yoram Vodovotz, Ashley Xia, Elizabeth L. Read, Josep Bassaganya-Riera, David A. Hafler, Eduardo Sontag, Jin Wang, John S. Tsang, Judy D. Day, Steven H. Kleinstein, Atul J. Butte, Matthew C. Altman (+2 others)
2017 Trends in immunology  
Emergent responses of the immune system result from integration of molecular and cellular networks over time and across multiple organs.  ...  However, connecting genetic variation and molecular mechanisms to individual phenotypes and health outcomes has proven elusive.  ...  We thank the many attendees and participants in the workshop for their input and Jill Gregory for creating the illustrations.  ... 
doi:10.1016/j.it.2016.11.006 pmid:27986392 pmcid:PMC5695553 fatcat:frk2t64wsnbilm4ojuuzcmxozi

Solving Very Hard Problems: Cube-and-Conquer, a Hybrid SAT Solving Method

Marijn J.H. Heule, Oliver Kullmann, Victor W. Marek
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
We present this and the underlying paradigm Cube-and-Conquer, a powerful general method to solve big SAT problems, based on integrating the "old" and "new" methods of SAT solving.  ...  A recent success of SAT solving has been the solution of the boolean Pythagorean Triples problem [Heule et al., 2016], delivering the largest proof yet, of 200 terabytes in size.  ...  A very basic backtracking SAT solver is the DLL-solver [Davis et al., 1962] . The DLL-algorithm uses unit-clause propagation (UCP) at each node to find the most basic inferences for SAT solving.  ... 
doi:10.24963/ijcai.2017/683 dblp:conf/ijcai/HeuleKM17 fatcat:sab7hccyanhcngia42ntarvlh4

The Strategy Challenge in SMT Solving [chapter]

Leonardo de Moura, Grant Olney Passmore
2013 Lecture Notes in Computer Science  
High-performance SMT solvers contain many tightly integrated, hand-crafted heuristic combinations of algorithmic proof methods.  ...  Bill McCune, Kindness and Strategy, by Grant Passmore I would like to tell a short story about Bill, of how I met him, and one way his work and kindness impacted my life.  ...  Jackson, Joost Joosten and Larry Paulson for helpful comments on a draft of this paper. We thank the referees for their many useful corrections and suggestions.  ... 
doi:10.1007/978-3-642-36675-8_2 fatcat:op5iarzvnvfkddz5ycsgyzo264

A package for solving parametric polynomial systems

Jürgen Gerhard, D. J. Jeffrey, Guillaume Moroz
2010 ACM SIGSAM Bulletin  
A Gröbner basis in a boolean polynomial ring, called a boolean Gröbner basis, is first introduced in [3, 4] with its computation algorithm in order to solve certain types of constraints over sets.  ...  Proceedings of the Seventh Asian Symposium on Computer Mathematics(ASCM2005), pp 145-148. [8] Sato, Y., Inoue, S., Suzuki, A. and Nabeshima, K. Boolean Gröbner Bases and Sudoku.  ... 
doi:10.1145/1823931.1823933 fatcat:zulpwzkc6jdgrebkevri3jmqye

Divide and Conquer: Towards Faster Pseudo-Boolean Solving

Jan Elffers, Jakob Nordström
2018 Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  
We propose a modified approach to pseudo-Boolean solving based on division instead of the saturation rule used in [Chai and Kuehlmann '05] and other PB solvers.  ...  The last 20 years have seen dramatic improvements in the performance of algorithms for Boolean satisfiability---so-called SAT solvers---and today conflict-driven clause learning (CDCL) solvers are routinely  ...  Acknowledgements We would like to thank Daniel Le Berre for many pleasant and enlightening discussions about pseudo-Boolean solving, and João Marques-Silva for helping us get an overview of relevant references  ... 
doi:10.24963/ijcai.2018/180 dblp:conf/ijcai/ElffersN18 fatcat:tw7e5ncfcfhgvipe5hbo2odz3y

A Survey on String Constraint Solving [article]

Roberto Amadini
2021 arXiv   pre-print
String solving approaches have become popular over the last years given the massive use of strings in different application domains like formal analysis, automated testing, database query processing, and  ...  String constraint solving refers to solving combinatorial problems involving constraints over string variables.  ...  For this reason, we tend to skim out the technicalities in favor of a more "high-level" vision of string solving, without however ignoring its theoretical foundations.  ... 
arXiv:2002.02376v8 fatcat:why6oeufmrbozbl22jlf7yivea

Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems

Yuxin Chen, Emmanuel J. Candès
2016 Communications on Pure and Applied Mathematics  
Empirically, we demonstrate that the computational cost of our algorithm is about four times that of solving a least-squares problem of the same size.  ...  We demonstrate that it is possible to solve unstructured random quadratic systems in n variables exactly from O(n) equations in linear time, that is, in time proportional to reading the data {a i } and  ...  C. is partially supported by NSF under grant CCF-0963835 and by the Math + X Award from the Simons Foundation. Y. C. is supported by the same NSF grant.  ... 
doi:10.1002/cpa.21638 fatcat:2q4yhghejvcsfljuekgexjescy

Parallel SAT-Solving for Product Configuration

Nils Merlin Ullmann, Carsten Sinz
2021 Zenodo  
This thesis presents parallel algorithms to solve SAT problems in the domain of product configuration.  ...  The necessity of reproducible solutions, despite using parallel algorithms, is considered and concepts to provide deterministic results are presented.  ...  Basically, a lookahead uses a variable which is propagated once for each truth value for a given Boolean formula F cnf .  ... 
doi:10.5281/zenodo.5152113 fatcat:lgpjojuoprc2hpdsqbsugzb7mm

Universal algorithms for solving the matrix Bellman equations over semirings

G. L. Litvinov, A. Ya. Rodionov, S. N. Sergeev, A. N. Sobolevski
2013 Soft Computing - A Fusion of Foundations, Methodologies and Applications  
This paper is a survey on universal algorithms for solving the matrix Bellman equations over semirings and especially tropical and idempotent semirings.  ...  However, original algorithms are also presented. Some applications and software implementations are discussed.  ...  =OR and ⊗ =AND: Boolean logic over the two-element set {0, 1}.  ... 
doi:10.1007/s00500-013-1027-5 fatcat:sdb66mm7pzfkdmeez4r2vix4oq

SAT-solving approaches to context-aware enterprise network security management

John Homer, Xinming Ou
2009 IEEE Journal on Selected Areas in Communications  
This paper presents an approach based on Boolean Satisfiability Solving (SAT Solving) that can reason about attacks, usability requirements, cost of actions, etc. in a unified, logical framework.  ...  within the context of various other requirements such as usability, ease of access, and cost of countermeasures.  ...  CONCLUSION We have introduced a methodology where the system security requirements can be converted to a Boolean formula and, using SAT solving techniques, one can quickly correct misconfigurations that  ... 
doi:10.1109/jsac.2009.090407 fatcat:tcbdthot3jafbbhzhwjg3du5na

Solving Finite Length Beam Equation by the Haar Wavelet Method

Dr.G. Hariharan
2010 International Journal of Computer Applications  
An operational matrix of integration based on the Haar wavelet is established and the procedure for applying the matrix to solve the differential equations is formulated.  ...  The beam is assumed partitioned into several finite elements and the deflection of the beam is required to be a positive quantity along the whole beam so that the related fundamental fourthorder ordinary  ...  The algorithm and procedure have been applied to use Haar wavelet method in solving ODEs. The result is comparable to the exact solution.  ... 
doi:10.5120/1349-1819 fatcat:pjuc2lvubzhjrjiynxjp3wfak4

Interaction Coverage Meets Path Coverage by SMT Constraint Solving [chapter]

Wolfgang Grieskamp, Xiao Qu, Xiangjun Wei, Nicolas Kicillof, Myra B. Cohen
2009 Lecture Notes in Computer Science  
It supports seeding with general predicates, which allows us to combine it with path exploration such that both interaction and path coverage goals can be met.  ...  Keith Stobie provided requirements and has been one of the driving forces to make CIT part of Spec Explorer.  ...  This work was supported in part by the National Science Foundation through award CCF-0747009.  ... 
doi:10.1007/978-3-642-05031-2_7 fatcat:r7ilwtf3jza3xb3sfnymh64ede

Four Problems Solved by the Probabilistic Language of Thought

Steven T. Piantadosi, Robert A. Jacobs
2016 Current Directions in Psychological Science  
approaches, (c) explains the origins of novel and complex computational concepts, and (d) provides a framework for abstraction that can link sensation and conception.  ...  Work using this framework demonstrates how the pLOT (a) refines the debate between symbols and statistics in cognitive modeling, (b) permits theories that draw on insights from both nativist and empiricist  ...  Acknowledgments We are extremely grateful to Jay McClelland and Jacob Feldman for providing detailed and insightful comments on this article.  ... 
doi:10.1177/0963721415609581 fatcat:rnoilgwblnagfh7d2scoikxhky

Design as Scientific Problem-Solving [chapter]

Dan Braha, Oded Maimon
1998 Applied Optimization  
CATEGORIES OF DESIGN REQUIREMENTS The most basic type of requirement is empirical, measurable or well-defined in nature.  ...  of design processes and the problem solving of scientific communities.  ...  The new requirements must then be integrated with the 'current' requirements and further analysis must be done.  ... 
doi:10.1007/978-1-4757-2872-9_2 fatcat:agky62sh3bgxpni746tco6wi2e
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